1. Technical Field
The present invention relates to a flexural resonator element, and a resonator, an oscillator, and an electronic device each having the flexural resonator element.
2. Related Art
In the related art, the fact that when a flexural resonator element is miniaturized, the Q value decreases and the flexural vibration thereof is disturbed is known. Here, the Q value is a dimensionless number representing the vibration state, and the higher it is, the more stably the flexural resonator element vibrates. This results from a thermoelastic effect which occurs when a relaxation vibration frequency that is inversely proportional to the relaxation time up to the equilibrium of temperature through heat transfer approaches a vibration frequency of the flexural resonator element. That is, when a flexural resonator element vibrates in the flexural vibration mode, an elastic deformation occurs, and the temperature of a compressed surface increases while the temperature of an expanded surface decreases. Thus, a temperature difference occurs in the inner portion of the flexural resonator element. The flexural vibration is disturbed by relaxation vibration of which the frequency is inversely proportional to the relaxation time up to equilibrium of the temperature difference through thermal conduction, and the Q value decreases.
In order to address this problem, JP-UM-A-2-32229 (see page 4 line 7 to page 5 line 3) discloses a technique in which a groove or a through-hole is formed in a flexural vibration portion of a flexural resonator element to prevent the transfer of generated heat from the compressed surface of a resonator to the expanded surface, thus suppressing changes in the Q value resulting from the thermoelastic effect.
Moreover, JP-A-2009-27711 (see FIG. 1 and FIG. 1a) discloses a piezoelectric tuning fork-type resonator (hereinafter referred to as a flexural resonator element). The flexural resonator element includes a base from which first and second parallel resonating arms extend, an enlarged portion (hereinafter referred to as a weight portion) having a flipper-like shape forming the free end of each of the resonating arms, and an excitation electrode for resonating each resonating arm, and a groove formed on at least one of the top or bottom surfaces of each of the resonating arms.
In the flexural resonator element having the groove as disclosed in JP-UM-A-2-32229, the groove prevents the diffusion (thermal conduction) of the heat generated by flexural vibration. Thus, it is possible to suppress thermoelastic loss which is a loss of vibration energy caused by thermal conduction occurring between the contracted portion and the expanded portion of a flexural resonator element resonating in the flexural vibration mode.
However, the flexural resonator element having the groove as described above has a portion which is disposed in a connection portion connected to the base of the resonating arm and in which larger stress occurs due to flexural vibration than other portions of the resonating arm. Thus, a large temperature difference occurs in the flexural resonator element when the temperature rises and falls.
Moreover, in the groove positioned in the connection portion of the resonating arm connected to the base, an excitation electrode is continuously formed on the surface thereof so as to extend from one side in the width direction of the resonating arm to the other side. Therefore, thermal conduction in the connection portion of the resonating arm connected to the base is accelerated by the excitation electrode that is formed of a metal having high thermal conductivity and formed on the groove in the connection portion. The present inventor has found a problem wherein the thermoelastic loss increases and the Q value decreases.
According to FIG. 1 of JP-A-2009-27711, the flexural resonator element has a slope portion (tapered portion) which is formed between the resonating arm and the base so that the distance between the groove and the outer edge of the resonating arm increases as it approaches the base from the resonating arm in plan view.
According to FIG. 1 and FIG. 1a of JPA-2009-27711, in the flexural resonator element, the excitation electrode formed in the groove extends up to a range corresponding to the connection portion and is formed in the inner wall of the groove so as to be continuous from one end in the width direction of the resonating arm to the other end thereof.